In mathematics, the root mean square (abbrev. RMS, RMS or rms) of a set of numbers is the square root of the set's mean square. Given a set x i {\displaystyle...

The root mean square deviation (RMSD) or root mean square error (RMSE) is either one of two closely related and frequently used measures of the differences...

square of the quantity being estimated. In an analogy to standard deviation, taking the square root of MSE yields the root-mean-square error or root-mean-square...

The mean square speed ⟨ v 2 ⟩ {\displaystyle \langle v^{2}\rangle } is the second-order raw moment of the speed distribution. The "root mean square speed"...

appropriate. Root mean square (RMS) amplitude is used especially in electrical engineering: the RMS is defined as the square root of the mean over time of...

In bioinformatics, the root mean square deviation of atomic positions, or simply root mean square deviation (RMSD), is the measure of the average distance...

statistical mechanics, the mean squared displacement (MSD, also mean square displacement, average squared displacement, or mean square fluctuation) is a measure...

{\displaystyle E(X^{2})} is also called the mean square. The square root of a mean square is known as the root mean square (RMS or rms), and can be used as an...

acceptable model fit. The root mean square residual (RMR) and standardized root mean square residual (SRMR) are the square root of the discrepancy between...

DC component) is assumed. The RMS voltage is the square root of the mean over one cycle of the square of the instantaneous voltage. For an arbitrary periodic...

value being predicted is continuously distributed, the mean squared error, root mean squared error or median absolute deviation could be used to summarize...

n]-x[m,n]\right|)} Measuring the average squared difference between two signals. Unlike the maximum error, mean squared error takes into account the overall...

related to the mean squared error, the equivalent for mean absolute error is least absolute deviations. MAE is not identical to root-mean square error (RMSE)...

sqroot(avg(square(a))) where square(x) = x*x; avg(y) = mean where n = 1 fby n+1; mean = first y fby mean + d; d = (next y - mean)/(n+1); end; sqroot(z)...

effect size estimator for multiple comparisons (e.g., ANOVA) is the Ψ root-mean-square standardized effect: Ψ = 1 k − 1 ⋅ ∑ j = 1 k ( μ j − μ σ ) 2 {\displaystyle...

arithmetic mean M 1 ( x 1 , … , x n ) = x 1 + ⋯ + x n n {\displaystyle M_{1}(x_{1},\dots ,x_{n})={\frac {x_{1}+\dots +x_{n}}{n}}} root mean square or quadratic...

^{(t)})^{2}={\frac {1}{D}}\sum _{i=1}^{D}(x_{i}^{(t)}-\mu ^{(t)})^{2}} . Root mean square layer normalization (RMSNorm) changes LayerNorm by x i ^ = x i 1 D...

mathematics, a square root of a number x is a number y such that y 2 = x {\displaystyle y^{2}=x} ; in other words, a number y whose square (the result of...

root mean square error (RMSE) is the square-root of MSE. The sum of squares of errors (SSE) is the MSE multiplied by the sample size. Sum of squares of...

associated concepts, such as the DRMS (distance root mean square), which is the square root of the average squared distance error, and R95, which is the radius...

computing a mean for each sample. The mean's standard error turns out to equal the population standard deviation divided by the square root of the sample...

calculating variance Errors and residuals Least squares Mean squared error Residual sum of squares Root-mean-square deviation Variance decomposition Mood & Graybill:...

electrical circuit. It is the product of the root mean square voltage (in volts) and the root mean square current (in amperes). Volt-amperes are usually...

mean inequality chain, state the relationship between the harmonic mean, geometric mean, arithmetic mean, and quadratic mean (also known as root mean...

The mean absolute scaled error has favorable properties when compared to other methods for calculating forecast errors, such as root-mean-square-deviation...

unit is the metre (m). Mathematically the radius of gyration is the root mean square distance of the object's parts from either its center of mass or a...

statistics, the coefficient of variation (CV), also known as normalized root-mean-square deviation (NRMSD), percent RMS, and relative standard deviation (RSD)...

computes the square root of the sum of squared amplitudes divided by the number of samples within the specified window used. With this root mean square amplitude...

{x}})^{2}} . The sample mean is also the best single predictor because it has the lowest root mean squared error. If the arithmetic mean of a population of...

harmonic mean, G is geometric mean, L is the logarithmic mean, A is the arithmetic mean, R is the root mean square and C is the contraharmonic mean. Unless...